The Black Mamba is considered the deadliest snake in the world it is therefore not a surprise to see that it is the codename for the world's deadliest assassin Beatrix Kiddo.
As all the member of the deadly viper assassination squad are named after snakes, the deadliest is named after the deadliest snake, therefore Beatrix Kiddo is codenamed the black mamba. However it appears that her former colleague Vernita Green is not happy about her being black mamba and says that she should've been codenamed black mamba.
Elle's black mambaEdit
Elle Driver another member of the deadly viper assassination squad uses a black mamba in order to frame Beatrix for the murder of Budd. During Budd's final moments, she reads out various facts about the snake as she is torturing/taunting him. Upon losing her last eye, the now blind and painfully confused Elle is left to the mercy of the black mamba inside the camper. However it appears that Elle survived as she is appearing in the third instalment of the Kill Bill franchise.
Elle Driver planted a black mamba in the suitcase full of cash that she gave Budd. It killed him by biting him in the face three times. It is possible that it may have killed Elle as well, since it was still alive while she was squirming in the camper, but this has not been confirmed.